Find the smallest number by which 85176 must be divided so that it becomes a perfect square

Given: A number $85176$.

To do: To find the smallest number by which 85176 must be divided so that it becomes a perfect square.

Solution:

Given Number$=8517$

$=\underline{2\times2}\times2\times\underline{3\times3}\times7\times\underline{13\times13}$

Here, all are perfect square, except $2$ and $7$.

Thus, the given number$( 8517)$ should be divided by $( 2\times7=14)$.